Vol. 7, No. 5, 2014

Download this article
Download this article For screen
For printing
Recent Issues

Volume 10
Issue 7, 1539–1791
Issue 6, 1285–1538
Issue 5, 1017–1284
Issue 4, 757–1015
Issue 3, 513–756
Issue 2, 253–512
Issue 1, 1–252

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
Cover
About the Cover
Editorial Board
Editors’ Interests
About the Journal
Scientific Advantages
Submission Guidelines
Submission Form
Subscriptions
Editorial Login
Contacts
Author Index
To Appear
 
ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Propagation of singularities for rough metrics

Hart F. Smith

Vol. 7 (2014), No. 5, 1137–1178
Abstract

We use a wave packet transform and weighted norm estimates in phase space to establish propagation of singularities for solutions to time-dependent scalar hyperbolic equations that have coefficients of limited regularity. It is assumed that the second order derivatives of the principal coefficients belong to Lt1Lx, and that u is a solution to the homogeneous equation of global Sobolev regularity s0 = 0 or 1. It is then proven that the Hs0+1 wavefront set of u is a union of maximally extended null bicharacteristic curves.

Keywords
wavefront set, wave equation, propagation of singularities
Mathematical Subject Classification 2010
Primary: 35A21, 35L10
Milestones
Received: 18 February 2014
Accepted: 11 April 2014
Published: 27 September 2014
Authors
Hart F. Smith
Department of Mathematics
University of Washington
Box 354350
Seattle, WA 98195-4350
United States